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In this article, we consider a von Karman equation with variable exponent nonlinearities wtt(x,t)+Δ2w(x,t)+|wt(x,t)|γ(x)−2wt(x,t)=[w(x,t),F(w(x,t))]+|w(x,t)|p(x)−2w(x,t)in a bounded domain Ω⊂ℝ2. We firstly discuss an existence result of solutions by utilizing Faedo‐Galerkin approximation technique. Then, we undertake an investigation of asymptotic stability to the solutions by making use of the multiplier method. [ABSTRACT FROM AUTHOR]

In this paper, the author establishes a sufficient condition for logarithmic nonlinearity in nonlinear evolution equations. Lian et al. (Nonlinear Anal. 184, 2019, 239–257) proved the existence and blow‐up of solution for the hyperbolic equations with logarithmic nonlinearity. However, there is a critical error in proving the local existence of the solutions. For this previous result to be correct, logarithmic nonlinearity needs additional conditions. We establish a sufficient condition for logarithmic nonlinearity in Lian et al. Moreover, we also give the condition of logarithmic nonlinearity to the parabolic equations. [ABSTRACT FROM AUTHOR]